Remark 4.3 A direct conclusion of 9.23.2 is that \(u(t,\gamma )\)  is Lipschitz continuous with respect to \(\gamma \) , and the continuity of \(u(t,\gamma )\)  with respect to \(t\)  is similar to the proof of Proposition 5.5 in Peng [1]}. There is no essential difference between the classical Lipschitz generator and the non-Lipschitz generator in our setting, so we leave out the proof of 9.14.1 here.

